MAY 1985
LIDS-P-1466
INFORMATION STORAGE AND ACCESS IN DECISIONMAKING ORGANIZATIONS*
by
Ghassan J. Bejjani
Alexander H. Levis
ABSTRACT
Information storage and access in decisionmaking organizations is
modeled using a Petri Net representation.
A centralizedr and a
decentralized database configuration are analyzed and their impacts on the
decisionmakers' workload assessed.
Organizational protocols are defined
and their criteria of acceptability presented. Protocols' key variables,
minimum allowable input interarrival time and response time, are determined
for two organizational structures: parallel and hierarchical. A numerical
example suggests the use of timeliness as a third organizational attribute
the first two being workload and peformance. It also demonstrates the
importance of updating coordination in evaluating the organization's
performance.
*This work was carried out at the MIT Laboratory for Information and
Decision Systems with support provided in part by the Office of Naval
Research under Contracts N00014-83-K-0185 (NR 274-349) and N00014-84-K-0519
(NR 649-003) and in part by the US Army Research Institute for the
Behavioral and Social Sciences under Contract No. MDA903-83-C-0196.
Morgan Stanley, 55 Water Street, New York, NY 10041
Laboratory
MA 02139.
for
Information
and
Decision
Systems, MIT,
Cambridge,
1.
INTRODUCTION
During the past decade, information theory has been applied to
and
analysis
evaluation
of
developed
First
organizations.
by
the
Shannon
(Shannon and Weaver, 1949), information theory matured into a mathematical
theory
in
its
own
right,
and
applied
was
human
(see Sheridan
decisionmaking
the
study
of
various
It was then used as a basic tool
communications systems (Gallager, 1968).
for modeling
to
and
1974,
Ferrel,
and
The Partition Law of Information (Conant, 1976) provided a
Drenick, 1975).
physical interpretation of the mathematical expressions derived by using
the n-dimensional version of the theory.
A
two-stage
information
theoretic
model
introduced by Boettcher and Levis (1982).
of
the
decisionmaker
was
Quantitative means for measuring
the human decisionmakers' workload and the organization's performance were
designed
under
a
set
of restrictive
effort (Hall and Levis, 1984;
assumptions.
Chyen and Levis, 1985;
Subsequent
research
Tomovic and Levis,
1984) was oriented towards relaxing some of those assumptions and resolving
more complex issues related to a realistic use of the decisionmaking model.
This paper addresses the issue that decisionmakers are not memoryless
(an assumption in the original model) and
that information storage and
service in most modern organizations.
acccess devices are actually put to
The study of databases in acyclical organizations is approched along two
directions:
(a) computation of modified activity terms that represent the
decisionmaker's workload and (b) consideration of time and delays in the
normal functioning of an organization.
separately but are
The two directions are developed
brought together in the illustrative example of the
last section.
Figure 1 shows the Petri Net representation (Tabak and Levis, 1984) of
the two-stage model of the nth member of an organization.
His input xn is
a component of a single vector source distributed by a set of partitioning
matrices
among
decisionmaker
all
the
decisionmakers
(Stabile and
Levis,
1984).
The
processes this input in the situation assessment (SAn) stage
2
DM"
unmin
on
no
i7r
Petri Net Representation of the nth Decisionmaker of the
Figure 1.
Organization
to determine or select a particular value of the variable zn that denotes
the situation.
He may communicate his assessment of the situation to other
members (zn °) and he may receive their assessments in return (zon).
This
supplementary information may be used to modify his assessment, i.e., it
may lead to a different value of zn denoted by zn
.
Possible alternatives
of action are evaluated in the response selection (RSn) stage.
The outcome
of this process is the selection of a local action or decision yn that may
be communicated to other team members or may form all
organization's response.
or
part of
the
A command input from other decisionmakers, v°n,
may affect the selection process.
The
situation
i=1,...,U).
assessment
stage
consists
of
U
algorithms
(fin,
The value taken by the variable un determines the algorithm to
3
distribution p(un).
be used, and is chosen according to the probability
Similarly, the choice of an algorithm in the RS stage is determined by the
variable Vn , with probability distribution p(vnlzn').
As a response
to the
handling
memory and information
need for
in
today's organizations, the concept of Decision Aids first appeared a litle
These devices are evolving into well-integrated
more than a decade ago.
Decision Support Systems (DSS) (Keen, 1981).
three main parts
information
terminal)
Decision
Support System.
program,
and
of a
management
The database is one of the
(Sprague, 1980;
a
Sprague and
machine-user
Carlson,
address the database and decisionmaker/machine
and
their
impact
on
the
other
two are
interface
1982).
an
(computer
This paper
will
interface issues from an
The database's
information theoretic point of view.
procedures,
The
storage and access
decisionmaker's
workload
and
performance levels, will be described.
2.
THE GENERAL DATABASE MODEL
The database model developed in this paper conforms to the traditional
definition of an information storage device:
from an external
source, it stores
it can receive information
it adequately, and it delivers
information, or part of it, whenever accessed by its users.
model adopted here consists of two stages
(see Fig. 2).
this
The Petri Net
The first stage,
transition C, receives an input from the decisionmaker who requests access
to the data.
This input represents the situation in which the user is.
Transition C determines then the nature of the information needed to cope
with that situation, and sends a query to the next stage, D.
Transition D
performs the actual search, and delivers the data to the decisionmaker at a
predetermined stage of his internal decisionmaking process.
DB
Figure 2.
c
Petri Net Representation of the General Database Model
4
Databases
can be
used in
Decentralized
either
configuration.
a
centralized
are
databases
or
defined
a
decentralized
as
here
individual
storage units, accessed exclusively by one decisionmaker, and holding and
It was
delivering information relevant to this decisionmaker's task only.
proved (Bejjani, 1985) that the increase in activity due to a centralized
However, there are important
or decentralized configuration were similar.
differences.
First,
the
time associated with
is much
the query process
shorter when the database is an individual one than when it is centralized.
In effect, in the former case, no irrelevant information is to be scanned
and then discarded, which happens in the latter case,
answer
to
its
centralized
database
It
updating.
stimuli
decisionmakers
can
structure
be
with
more
is
is
updated
equally
timely.
in
that
one
recent
However,
an
allows
for
it
operation,
information,
the system's
and
of
advantage
more
convenient
providing
whereas
a
all
the
decentralized
databases require a much greater updating effort to obtain the same result.
This paper will develop information theoretic aspects of
the centralized
databases and discuss the decentralized case briefly (for a comprehensive
comparison of the two configurations, the reader is referred to Bejjani,
1985).
2.1
Centralized Databases
A centralized database is a database shared by all
organization.
terminals
It
is
allow the
physically
located
decisionmakers to
in
one
access
place,
members
and
of the
individual
it independently.
In
the
Petri Net representation, a centralized database is modeled as one unit,
comprising several transition Cltransition D sequences.
databases, one for the SA stage,
called DBSA,
DBRS.
Cn in DBSA
The
inputs
to transition
There are two such
and one for the RS stage,
are
the
inputs
to
the
nth
decisionmaker, xn , and the variable un indicating the SA algorithm he is
about to use
(see Fig. 3).
Transition Cn emits
then a message
towards
transition Dn that carries a query for the information needed for DM n to
process xn through
the selected SA algorithm.
Dn in
turn delivers
the
requested data, dnA, to the decisionmaker, who receives it as an input to
the algorithm he is using.
applied to the RS stage.
The usage of DBRS follows a similar rationale
DMn
_
un
n
B
Mn
- n
v" :
,
:
n
'---
n
Vh
dn :
:
onn
E:RS
_
I
·
BSA
In
y"
.
.A
C .
dD
0D
dRS
*
0
:
:
Figure 3. Petri Net Representation of DMn Using Centralized Databases
The use of databases has a significant impact on the decisionmaker's
workload, as can be seen in the following development.
Activity rate terms
are derived by applying the Partition Law of Information Rates
1976)
to
the
decisionmaking
model
used
For
here.
a
more
(Conant,
complete
description of the calculations, the reader is referred to Bejjani (1985).
The modifications to
the basic model
are due
to
the
presence of
two
supplementary variables, dnA and dnS, and to their relationship with the
existing structure.
For simplicity, the superscript n will be omitted in
the following equations whenever confusion may not arise.
6
Throughput Rate:
F -
Ft T(xdSAz
on
onxno
:uz
vdRS y)
,zv
pZpVpy
_no
(1)
Blockage Rate:
(2)
Fb = H(x,dsA,z°nv°ndRs) -Ft
Noise Rate:
F
n
LH_(v)
z
= H(u) +
(3)
Coordination Rate:
U
(
Fc =
H(pi)) + H(z)
(p(x,ds)) +
L c SA ~SA
i=!
+ A (p(z,zon)) + -B (p(,von))
V
(g+j (P(idRs)) +
Q
+
j=l
+H(z)
+ H(E)
U
RS
RS
H(pj)) + R(y)
n
+)
+ H(Z,V) + T(xdsA:z
on
on
.....
on vol)
v n
T_(x,dsAzn
:dRs)
(4)
pj = p(v=j)
(5)
+ TZ, (x,dsAz°n v
where
Pi = p(u=i)
;
7
H(p) = plogzp + (1-p)logz(1-p)
(6)
and ai is the number of variables of the algorithm i that are reinitialized
at each iteration.
The symbol rSA designates the mean interarrival time of
the input to the SA stage.
the
RS
stage.
equations, if
The
the
mean
sRS has an equivalent meaning with respect to
input
interarrival
interarrival
source (Hall, 1982).
time
time
can
is not constant,
The functions gic ,
cU+j
be
used
in
the
by regulating
the
gA and gB are the individual
coordination rate functions of the SA, A, B, and RS algorithms, and are of
the following form:
ai
u
<wgo
(W ) (
u
wl
(7)
j=1
The terms H(z), H(Z), H(R,V) in (4) can be interpreted to represent
the direct coordination rate between subsystems, through the fact that one
subsystem's
output
is
between the subsystems
Tz(x,dsA:zon)
another's
input.
is accounted
represents
the
However,
indirect
coordination
for by the transmission rate terms.
coordination
relationship between x and dSA, and zOn .
rate
that
is
due
to
the
Indeed, if the inputs to DMn and
those to the rest of the organization (RO) are related, or if dnA and dmA,
m A n, are not totally independent, due to the structure ofthe storage or
the updating process in the centralized database, then zon can bring to SA
information about the inputs
to the
system that is not contained in z.
Similar interpretations hold for the other
two
transmission rate terms.
The term TZ,v(x,zon,dsAv°n:dRs) raises the question of the relationship
between dSA and dRS, i.e., whether the situation assessment database (DBSA)
and the response selection one (DBRS) are related.
2.2
Decentralized Databases
A decentralized database structure is shown in Figure 4.
The only
difference with respect to Figure 3 is the presence of only one transition
Cn/transition Dn
sequence
per database, which models the exclusive use of
8
DMn
Uzn
nz
n
yn
71IR
Petri Net Representation of DMn Using Decentralized Databases
Figure 4.
each database by a single decisionmaker.
Apart from that,
decentralized
databases are assumed to function in exactly the same manner as centralized
ones.
2.3
Fixed Databases and the Memoryless Model
The results in section 2.1 were derived assuming the data dSA and dRS
to be variable quantities.
However,
it might very well be the case that
dSA and dRS are fixed, either because the databases are never updated or
because the values taken by dSA and dRS remain valid during a very long
time, compared to the mean input interarrival time.
In this simple case,
the database's direct contribution to the decisionmaker's activity rate is
null, and the expressions developed above become similar to those derived
in the basic memoryless decisionmaker case.
eliminating
the
variables
dSA
and
dRS and
9
They are derived by simply
the
input
variables
to
the
databases
from the equations,
which shows
that
the
reduction
from
the
database-equipped model to the memoryless one is consistent.
3.
PROTOCOLS AND THEIR APPLICATION TO ORGANIZATIONAL STRUCTURES
3.1
Definition of Protocols and Determination of Their Key Variables
elementary tasks have
as
between
of the chronological order in which
the description
A protocol is
to
two or more
be
of
performed within one decisionmaker as well
them.
Determination
of
procotols
is
a
fundamental design problem for organizations in general, and of updatable
database-equipped
operations
ones
for each
in
particular.
decisionmaker
Indeed,
are not
clearly
if
the
sequences
defined,
and
if
of
the
updating tempo of the database does not take these sequences into account,
chaos can result.
In brief,
the
situation could arise where
different
decisionmakers would be accessing different databases at different times,
with different levels of accuracy and relevance of the data, in order to
process the same input.
Since the Petri Net representation
(Tabak and Levis,
1984)
clearly
illustrates the organization's protocol as defined above and since a key
notion in the definition of a protocol is the amount of time involved at
each step of the decisionmaking process, an acceptable protocol for a given
organization will consist of its Petri Net representation supplemented with
the allocation of a processing time
to each transition.
The processing
time in fact represents the maximum allowable duration of a transition for
the organization to function in an orderly fashion, following its operating
protocol.
Assumptions:
In
devising
an
acceptable
protocol
for
the
kind
organizations dealt with here, the following assumptions are made:
(1)
- the source emits the input X with a constant interarrival time
(2)
- the various transitions have constant processing times.
(3)
- communication between transitions is instantaneous.
10
of
(4) - any transition can process an incoming input as soon as it has
finished processing the previous one, and no sooner.
(5) - no queueing is allowed at any stage of the process.
Assumptions (1) and (2) are a corollary of the broader assumptions
that the whole system operates in
Assumption (3) states in
steady state.
fact that all the decisionmaking occurs within the transitions, and that no
processing time is allocated to places.
'pipe-line effect' into words;
this
(4) is putting the
Assumption
the information flow
assures that
Assumption (5) is a prerequisite to the
through the system is continuous.
study of information
application of Petri Net theory to the
theoretic
in effect, when queueing takes place, two or more
decisionmaking models:
Since transitions do not
different tokens can coexist in the same place.
have any means of recognizing priorities in choosing one token as an input
out of the same place, the queue cannot be managed, and the organization's
protocol is transgressed.
(For a relaxation of this assumption, see Jin,
1985).
Under assumptions (1) to (5), two necessary conditions
Proposition:
for an organization's protocol to be acceptable are:
every transition in the system must have a processing time smaller
than or equal to the mean input interarrival time.
- the total amount of time spent by a token in one place cannot exceed
the mean input interarrival time.
necessary
Both
provide
conditions
symmetric
a
tool.
analytical
Indeed, if the processing times of the transitions in the system are fixed,
time for the organization
then the minimum admissible input interarrival
can be determined:
it is equal to the greater of two quantities:
maximum
time
processing
and
organization,
Determining
this
the
maximum
minimum
on
the
Petri
time
any
token
present
interarrival
time
is
net
diagram
spends
a
very
in
of
any
useful
the
that
place.
way
of
comparing the effectiveness of different organizational structures in a
given context.
The second necessary condition applies in cases of
11
organizational
interactions where one decisionmaker sends some information to another and
cannot proceed
before receiving a message
the
Thus,
back.
proposition
provides a way of determining the upper limit of the response time of this
decisionmaker,
other
being
else
everything
This
fixed.
will
be
made
clearer in the next section.
As a last comment, one should realize that the use of the proposition
is not restricted to decisionmaking organizations.
are
relevant
to
any
information
acyclical
In fact, its arguments
processing
structure
where
Assumptions (1) to (5) are satisfied.
3.2
Construction of Protocols for the Centralized Case
In this section, the proposition will be used to develop protocols for
database configuration.
two particular organizations using a centralized
The basic quantity for each organization is a, the processing time of any
SA
or
RS
It
transition.
is
assumed
to
be
identical
for
all
such
transitions in both organizations, and it will be the unit used for all
quantities computed here.
Furthermore, v is assumed to be greater than the
processing time of other types of transitions,
on the grounds
decisionmaking takes place in SA and RS transitions
The database's response time is
that more
than in the others.
assumed to be v as well.
Parallel Organizational Structure
In a parallel organizational structure, decisionmakers are linked by
they do not formally issue commands to
somewhat symmetrical relationships:
each other, and they can share information at all stages according to preestablished operating
The
procedures.
parallel structure
considered
in
this work is a three-person organization, (Fig. 5) called 'Organization P"
from here on.
DM1 and DM 3 use only one SA algorithm and two RS algorithms
each, and DMs has the choice between two SA algorithms, whose output can be
processed by only one RS algorithm.
the model,
due to
The command input von is absent from
the non-hierarchical structure;
the decisionmakers
however share information about their situation assessments.
12
do
Organization P uses
databases,
two centralized
DBSA and DBRS;
acceptable protocol for this organization has been derived and is
(RT), the time
I, and the organization's total response time
it allows,
between
the
arrival
of
fi
and
input
the
corresponding response, which is equal to
the
generation
C'
a
rh
z\
A
D
13
X2
of
19v/3.
Al3
z 2
7/'
given in
Its main characteristics are the minimum interarrival time (IT)
Figure 5.
interval
An
'
O'
~r/3dA
-2r/3
rj3
21
r/3
[DMBRS
12T/3
f
I
()d3 |
f3r/3
2 r/3
lSA /
M3
3
23
13
hiZ
Hierarchical Organization Structure
A hierarchical organizational structure allows decisionmakers to have
an influence
on each other's response selection.
represented by a command input, von.
This influence can be
The hierarchical structure analyzed
here is a three-person organization, known as organization H, equipped with
centralized databases as shown in Figure 6.
flf~
B'
~~Z
--
12/3
---
2
C2
2
D
DBRS
7r
DBSA
3
/3
"/3d`S'
DM
X3
T~j
dr
A2
2
-1C
Y
r3 r/3.2,/3
,
-/33
32
(
Z
jt
t
DM 3
Figure 6.
Protocol of Organization H Using Centralized Databases
14
Y3
Organization H consists of two decisionmakers who actually contribute
to its output, DML and DM', and one coordinating decisionmaker, DM2, who
analyzes DM1 's and DM2's situation assessments in order to issue a command
to them that carries his instructions about the way the organization's
response
should
be
DM1
constructed.
is
not
in
contact
with
the
environment, therefore he does not need an SA stage, neither do DM2 and DM3
need an information fusion transition,
A.
The
three decisionmakers
in
organization H have each two RS algorithms.
One acceptable protocol for organization H is that represented in
The minimum interarrival time, 11v/3, is much greater than for
Figure 6.
organization P.
This is due to the relationship between transition fx and
DM , where
information
the
coming
out of fx has to be processed by all
DM2's transitions before transition B x can be fired and the last token
leaves
the
place
zL.
Application
of
the
argument
symmetric
of
the
proposition's necessary conditions determined the mean interarrival time
The organization's response time is calculated quite simply in
as 11i/3.
this case, by adding all processing times along the path followed by the
original input and is 8,.
For more complex organizations, the System Array
approach is preferable for computing time delays (Tabak and Levis, 1984;
Jin, 1985).
3.3
Construction of Protocols for Decentralized Case
It was pointed out in section 2.2 that the only salient differences
between a centralized and a decentralized structure as defined here pertain
to transition D's processing time and the establishment of satisfactory
updating.
In this section, transition D is assumed to require a total time
of v/3, which is half what was needed in the centralized configuration.
Again, this number depends greatly on the nature of the organization's
decision support system.
Acceptable protocols for organizations P and H with
databases
are given in Figures 7 and 8, respectively.
decentralized
The minimun inter-
arrival time IT and the response time RT for each organization are r and
15
12=/3 for the parallel one and 10t/3 and 7v for the hierarchical one.
The reduction in the IT and RT, when compared to
the centralized
cases, is due entirely to the shorter response time of the database.
DBSA1
DBRS I
D
'
x
DBSA 2
X2 I
C
X
DM2
2
gX3
2o
]t
Alhi
DBRS 2
D2
2
SA3
r73
S
M
Md~
1
1
Z
) z22
Z1
,
c
r/R
02
do
r3
S
WE~k
fZ
Y
Ez23
zz3
-
hx
f3 16
DM3
r/3
0MSA 3
SA
-z3
r/ _ rS3
DSRS3
h3
Figure 7. Protocol of Organization P Using Decentralized Databases
16
32r/3
f r
L
-/S
A2
3 S
t~
h~A
DBRS2
2-
21
DBRSL
-
DM3
Figure 8. Protocol of Organization H Using Decentralized Databases
3.4
Remarks
Each protocol in the previous sections has been derived under some
very specific conditions, in order to make different organizations and
These
different database structures comparable along the same criteria.
results are contingent upon using similar transition processing times for
both organizational structures.
17
17
2r!
The minimum allowable input interarrival time is much greater for a
hierarchical organization than for a parallel one.
This follows from the
more complex sequences of tasks that have to be performed in a hierarchical
organization before a new input can be handled.
The total response time is
also greater for organization H than for organization P, and the difference
is due again to the increased complexity.
The
second
observation
is
that,
whatever
the
organization,
a
decentralized database structure leads to improved performance with respect
to time.
In organization P, the decentralized structure leads to an 11%
improvement in the response time over the corresponding centralized one,
while in organization H its leads to improvements in both IT and RT of 9%
and 13% respectively.
These results are due to the basic premise that
decentralized databases takes less time to perform the data query process
than
centralized
ones
do.
(The
numerical
results
of
the above
paragraphs are summarized in Table 1).
TABLE 1. TIME CHARACTERISTICS OF ORGANIZATIONS P AND H
Centralized DB
Decentralized DB
IT(P)
I
IT(H)
11-/3
10c/3
RT(P)
19-13
17'c/3
RT(H)
8-
7-
IT = Minimum Allowable Interarrival Time; RT = Response Time
18
two
4.
AN ILLUSTRATIVE EXAMPLE
4.1
In
Description of the Organizations Used
this
section,
tactical
organizations,
one
parallel
and
one
hierarchical, are used to address the issues that arise in the qualitative
evaluation of organizations, the problems raised by a lack of coordination
between several individual databases, and the trade-off between performance
and timeliness.
(The example is developed in its
entirety
in Bejjani,
1985).
The first organization is the parallel one (Organization P) in Figure
5.
It consists of three naval battle groups defending a maritime front.
The first group, DM 1,
center, and DM
signals
planes).
holds
one extremity of the
the other end.
emitted
by
front, DM2 holds
the
The inputs received by the organization are
unidentified
platforms
(submarines,
surface
ships,
The different decisionmakers' tasks are to attempt to identify
the source of these signals
(enemy or friends) in the SA stage, and to
select the appropriate response (fire, request identification, or take all
measures required to face an attack) in the RS stage.
The
SA
database
provides
information,
obtained
from
intelligence
sources, that describes the codes the enemy could use when emitting the
kind
of
signals
received by
organization
P.
This
information
will
compared to the actual input to determine the latter's identity.
be
The RS
database, DBRS, informs the decisionmakers about the level of alert present
in their area at each iteration.
The second organization is the hierarchical one (Organization H) shown
in Figure 6.
1
DM
and DM
response.
received
3
The context is the same as for organization P, but here only
actually receive
any external
signals or
select
an
active
DM2 is a coordinator who, based upon the situation assessments
from
DM1
and
DM3 ,
gives
instructions about
should be selected by either of them.
is the one defined for organization P.
19
what RS
algorithm
The organization's overall mission
4.2
Results
A primary feature of the example is its numerical simplicity:
all the
variables of the system are determined using binary logic based
comparison of
quantities;
there
are
no
actual
computations.
on the
Detailed
definition of the variables and the algorithms for the case of a single
decisionmaker has already been presented (Boettcher, 1981).
The basic step
in the computation of the performance-workload pair (J,G) is determining
the pure
1983).
strategies
In
the
present
cases
at
in
hand,
the
organization
(Levis
each
DM
pure
has
two
and
Boettcher,
strategies,
each
obtained by the exclusive use of one algorithm (no decisionmaker here has,
in any stage, more than two algorithms from which to
choose).
rates are a better measure of the decisionmakers' workload
Activity
than absolute
activity, because of the time constraints present in real-world situations.
The following equation applies here:
Fi= i=
i = 1,2,3
for either organization.
(8)
The performance measure J is the expected value
of the cost the organization incurs when it does not produce the correct
response for
a given
strategy and
the
input.
The
corresponding
(J, G1 , 5G,53) space.
workloads
Gi determined
by
each
pure
performance level J are plotted in the
Then, the performance-workload (P-w) locus for each
DM is constructed where all possible mixed strategies are considered as
linear combinations of the pure ones.
The graphs thus obtained are the
projections of the overall (P-W) locus of the organization on each of three
planes:
(G3 ,J).
(G',J), G1 ,J),
1
Because the input is perfectly symmetric,
3
as well as DM 's and DM 's roles in each organization, only the projections
for DM1 and DM' are shown.
The
use
illustrating
of
activity
very
clearly
(Figs. 9 and 10).
H;
rates
in
this
the tradeoff
instance
between
has
the
timeliness
effect
and
of
workload
The performance of organization P is better than that of
the performance index for P takes values between 0 and 0.9 for P but
20
between 1.2 and 4.5 for H.
However, the workload of the members of P is
much higher than that of H, namely, it varies between 8.1 bits/sec and 11.6
for P, while it is only 1.2 and 2.7 for H. Measuring workload in terms of
activity rates gives
organization H a significant advantage as
keeping the decisionmakers' workload below a given maximum
rationality constraint) is concerned.
far as
(the bounded
However, another tradeoff appears
here that involves the notion of timeliness.
In effect, since in this
example workload is a decreasing function of the mean interarrival time,
Eq. (8), low workload levels are obtained by allowing a high IT, which
penalizes the organization in terms of its timeliness.
Thus, workload is
reduced in H, but timeliness is sacrificed.
Another consideration of interest is
the effect
of poor updating
coordination on the organization's performance when decentralized databases
are used (e.g., Figures 7 and 8).
The impact of two different updating
sequences on performance is reflected on the
scheme, DM1 's and DM''s
RS databases are assumed to be updated, at s + 0,
in coordination with the input arrival.
at
New
x
+ x,
(P-W) loci. In the first
DMX's DBRS, however, is updated
with a delay of v over the input to which the data correspond.
performance
levels
for
each pure organization strategy were derived
and a performance-workload locus was drawn (see Fig. 11(a)).
The main
effects are the upward movement of the original locus, and a degradation in
performance: the range of J is from
the
perfectly
coordinated
(or
0.35 to 1.0 as opposed to 0 to 0.9 for
the
centralized)
database
case;
this
represents a drop of 29% in the average performance of the organization.
A second scheme exhibits a less coordinated updating sequence:
is updated at v + O, DBRS' at v + x, and DBRS 3 at s + 2v.
DBRS1
DMx and DM3
both now have a greater propensity to make the wrong decision, and the
resulting (P-W) locus is presented in Fig. 11(b).
The best performance
(lowest J) is now 0.8, which is very close to what the worst performance
was in the coordinated case, and the worst performance level is 1.2.
The
range of possible performance levels has shrunk further, and the drop in
average performance with respect to the original case is 68%.
21
J
4.5
4
3.5
3
2.5
2
1.5
DM
1
0.5d'
0 4
I
4.5
5
I
I
5.5
6
I
I
6.5
7
I
I
7.5
8
I
8.5
I-
9
9.5
lO 10.5
t1
11.5G1
J
4.5
4
3.5
3
2.5
2
1.5
DM 2
0.5
4
4.5
5
5.5
Figure 9.
6
6.5
7
7.5
8
8.5
9
9.5
10 10.5
(P-W) Loci for P Using Activity Rates
22
11
11.5
J
4.5
4
3.5
3 _
DM 1
2.5
2
1.5
0.5
_
0
i
I
!
0.5
1
I
t
1.5
I,
,
I
2
2.5
3
I
3.5
4
4.5
'5
I
I
5.5
6
J i
4.5
4
3.5
3
DM 2
2.5
2
1.5
0.5
0
0.5
1
Figure 10.
1.5
2
2.5
3
3.5
4
4.5
5
5.5
6
(P-W) Loci for H Using Activity Rates
23
6.5
d
4.5
43.5
3
2.5
2
1.5
0.5
0'4
4.5
5
5.5
6
6.5
7
7.5
8
8.5
9
9.5
10 10.5
11
11.5
6.5
7
7.5
8
8.5
9
9.5
10
11 II.5
JG
4.5
4:
3.5
3
2.5
2_
1.5
_
I
0.5
0 4
4.5
Figure 11.
5
5.5
6
(P-W) Loci for DM1 in
24
10.5
P with Uncoordinated Databases
G
Let the transition processing time be equal to v seconds.
will be v
seconds
as well, and
IT(H)
11/3
depending on the database configuration).
seconds
Then IT(P)
(or 10/3
sec.,
In any event, IT(H) is much
greater than IT(P) and may handicap organization H if it has to respond to
threats arriving at a high rate.
As an example, consider a wave of enemy
planes attacking the battlegroup:
processing
every
input
through
If no defense can be initiated without
the
SA
stage,
then
the
anti-aircraft
batteries cannot shoot at a rate higher than one missile every 3.6v sec.
If a new threat arrives once every v seconds, then P is an adequate
structure, while H is far from being one.
An additional disadvantage of
organization H appears when response times are taken into account:
the
battlegroup will need 8S seconds to fire on a threat after it is detected;
this might be too long if the threat is very close to the battlegroup when
its presence is detected.
When the platforms that the organization has to deal with are slower
units,
like
submarines
disadvantage
is
less
or
surface
ships,
organization
H's
timeliness
critical, because of the longer time available
for
constructing an adequate response and because of the smaller threat arrival
rate.
In fact, the latter can be so small as to make any difference
between IT(P) and IT(H) seem irrelevant.
Since the organizations designed
in this example have to deal with both slow and fast threats, one has to
consider
the
relative
probability
of
being
attacked
by
fast or
slow
threats, and weigh it by the expected costs in each alternative during the
evaluation of the two organizational structures.
5. CONCLUSION
In this paper, the use of database networks was introduced into the
organization,
in
decentralized.
Information theoretic aspects of data storage devices were
analyzed.
two
alternative
configurations:
centralized,
and
Time-related consideration were presented and used to create new
criteria for the evaluation of the organization.
the major theoretical results.
25
The example illustrated
6. REFERENCES
'Information Storage and Access in Decisionmaking
Bejjani, G. J.,
Organizations,' M.S. Thesis, LIDS-TH-1434, Laboratory for Information and
Decision Systems, MIT, Cambridge, MA, January 1985.
Boettcher, K. L. "An Information Theoretic Model of the Decision Maker,"
M.S. Thesis, LIDS-TH-1096, Laboratory for Information and Decision Systems,
MIT, Cambridge, MA, June 1981.
Boettcher, K. L. and A. H. Levis, 'Modeling the Interacting Decisionmaker
with Bounded Rationality,' IEEE Trans. on Systems, Man, and Cybernetics,
Vol. SMC-12, No. 3, May/June 1982.
Chyen, H. H-L, and A. H. Levis, 'Analysis of Preprocessors and Decision
Aids in Organizations,' to be presented at the 2nd IFAC/IFIP/IFORS/IEA
Conference on Analysis, Design, and Evaluation of Man-Machine Systems,
Varese, Italy, September 10-12, 1985.
Conant, R. C., 'Laws of Information Which Govern Systems,' IEEE Trans. on
Systems, Man, and Cybernetics, Vol. SMC-6, No. 4, April 1976.
Cothier, P. H., and A. H. Levis 'Assessment of Timeliness in Command and
Control,' LIDS-P-1454, Laboratory for Information and Decision Systems,
MIT, Cambridge, MA, April 1985.
Drenick, R. F., 'Organization and Control,' Directions in Large Scale
Systems, Y.C. Ho and S. K. Mitter, Eds., Plenum Press, New York, 1976.
Gallager, R. G., Information Theory and Reliable Communication, John Wiley
and Sons, Inc., New York, 1968.
Hall, S. A., 'Information Theoretic Models of Storage and Memory,' MS
Thesis, LIDS-TH-1232, Laboratory for Information and Decision Systems, MIT,
Cambridge, MA, June 1982.
Hall, S. A., and A. H. Levis, 'Information Theoretic Models of Memory in
Human Decisionmaking Models,' Preprints of the 9th World Congress of IFAC,
Vol. VI, Budapest, Hungary, July 2-6, 1984.
Jin, V. 'Delays for Distributed Decisionmaking Organizations,' M.S. Thesis,
LIDS-TH-1459, Laboratory for Information and Decision Systems, MIT,
Cambridge, MA, May 1985.
Keen, P. G. W., 'Value Analysis: Justifying Decision Support Systems,' MIS
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University of Illinois Press, 1949.
26
Sheridan, T. B., and W. R. Ferrell, Man-Machine Systems, MIT Press, 1974.
Sprague, Jr., R. H., 'A Framework
Quarterly, December 1980.
for
the
Development
of
DSS,' MIS
Sprague, Jr., R. H. and E. D. Carlson, Building Effective Decision Support
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Stabile, D. A. and A. H. Levis, 'The Design of Information Structures:
Basic Allocation Strategies for Organizations,' Large-Scale Systems, Vol.
6, 1984, pp. 123-132.
Tabak, D. and A. H. Levis, 'Petri Net Representation of Decision Models,"
Proc. 7th MIT/ONR Workshop on C3 Systems, LIDS-R-1437, Laboratory for
Information and Decision Systems, MIT, Cambridge, MA, December 1984.
Tomovic, M. M., and A. H. Levis, 'On the Design of Organizational
Structures for Command and Control,' Proc. 7th MIT/ONR Workshop on C s
Systems, LIDS-R-1437, Laboratory for Information and Decision Systems, MIT,
Cambridge, MA, December 1984.
27